Exploring the set-theoretical structure of objects by additive trees

Arrangements of feature sets that have been proposed to represent qualitative and quantitative variation among objects are shown to generate identical sets of set-symmetric distances. The set-symmetric distances for these feature arrangements can be represented by path lengths in an additive linear tree. Imperfect versions of these feature arrangements are proposed, which also are indistinguishable by the set-symmetric distance model. The distances for the imperfect versions can be represented by path lengths in an additive imperfectly linear tree. When dissimilarities are defined by the more general contrast model and a constant may be added to proximity data, then for both the perfect and imperfect arrangements an additive tree analysis obtains a perfect fit with an imperfectly linear tree. However, in the case of the contrast model also the distinction between the perfect and imperfect arrangements disappears in that also for the perfect arrangements the resulting tree need no longer be linear.The author is grateful to Mathieu Koppen for detailed comments on an earlier version of this article.     

Pitch distribution,melodic contour or both? Modeling makam schema with multidimensional scaling and self-organizing maps

Experienced listeners internalize musical tonal knowledge via statistical learning of pitch distributions as a result of exposure to musical environment. Cross-cultural studies of music cognition offer new perspectives to investigate the acquisition of tonal schema. Makam music is a rich musical system characterized by modal structures defined by micro-tonal pitch sets, and melodic progression patterns (aka seyir features). Makam schema is possibly acquired by internalizing the seyir in addition to pitch features. In the current study, we examined whether an ideal model of makam schema is built with multidimensional scaling analysis and with self-organizing maps (SOMs). We were interested in whether statistical information about seyir features, in addition to pitch distributions, would form an acceptable makam schema model. We qualitatively analyzed topographical organizations in the models to understand whether they reflect complex relations between makams. Multidimensional scaling analyses did not produce an acceptable model for makam schema. The SOM trained with pitch distributions provided an adequate model for makam schema. However, the SOM trained with both pitch distributions and seyir features was better in capturing the complex relations between makams. Further behavioral research is necessary to understand whether melodic progression patterns are intrinsic features of the tonal knowledge of the experienced listeners of makam music.     

On Modal μ-Calculus and Non-Well-Founded Set Theory

A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal -calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.     

知识图对阅读的作用研究现状述评

知识图作为辅助阅读的一种方式,其辅助作用已为大量的研究所证实。本文介绍了知识图的概念和种类及其影响因素等方面研究的基本发现和结论。但目前对知识图作用的研究还停留在对辅助作用的方式的探讨上,对机制问题的研究数量和质量上都需加强。     

Representing Spatial Structure Through Maps and Language: Lord of the Rings Encodes the Spatial Structure of Middle Earth

Spatial mental representations can be derived from linguistic and non‐linguistic sources of information. This study tested whether these representations could be formed from statistical linguistic frequencies of city names, and to what extent participants differed in their performance when they estimated spatial locations from language or maps. In a computational linguistic study, we demonstrated that co‐occurrences of cities in Tolkien’s Lord of the Rings trilogy and The Hobbit predicted the authentic longitude and latitude of those cities in Middle Earth. In a human study, we showed that human spatial estimates of the location of cities were very similar regardless of whether participants read Tolkien’s texts or memorized a map of Middle Earth. However, text‐based location estimates obtained from statistical linguistic frequencies better predicted the human text‐based estimates than the human map‐based estimates. These findings suggest that language encodes spatial structure of cities, and that human cognitive map representations can come from implicit statistical linguistic patterns, from explicit non‐linguistic perceptual information, or from both.     

Applying matrix factorization techniques to compare experts’ categorization process during case formulation task performed by concept maps

The aim of this paper was to present a method to enable the analysis of the process of categorization of patients’ testimonials and the comparison of individual categories created by professionals. A complex diagnostic task (case conceptualization) was employed to study the categorization function in professional thinking. Two groups of psychotherapists (30 people in each group) served as subjects of the research. The main objective of the study was to find an appropriate representation of concept maps enabling a comparison of both the categories and the structures between experts. In the comparison process, only the information about the premises justifying each given category was taken into account and represented by a concept-testimonials matrix. Three different elements weighting schemes and matrix factorization-based unsupervised clustering methods were analyzed in the context of consistency and ability to establish main semantic groups of concepts common to the majority of experts. Moreover, special attention was paid to determining the number of main semantic classes. The study showed that even the used representation was similar to the task of documents indexing there was some discrepancy. The highest accuracy in generating main semantic groups was achieved using the PCA and K-Means (nKM) (the average false positive rate in clusters was 32%). This method outperformed Tempered PLSA (the average false positive rate per cluster was 52%). It was demonstrated that in analyzed task the nKM method allowed comparing the similarity of concepts even when they were created by various experts using different conceptual apparatus.     

Spatial knowledge acquisition from direct experience in the environment: individual differences in the development of metric knowledge and the integration of separately learned places

Existing frameworks for explaining spatial knowledge acquisition in a new environment propose either stage-like or continuous development. To examine the spatial microgenesis of individuals, a longitudinal study was conducted. Twenty-four college students were individually driven along two routes in a previously unfamiliar neighborhood over 10 weekly sessions. Starting Session 4, they were also driven along a short connecting route. After each session, participants estimated spatial properties of the routes. Some participants' knowledge improved fairly continuously over the sessions, but most participants either manifested accurate metric knowledge from the first session or never manifested accurate metric knowledge. Results are discussed in light of these large individual differences, particularly with respect to the accuracy and development of integrated configurational knowledge.     

Beta-MPT: Multinomial processing tree models for addressing individual differences

Traditionally, multinomial processing tree (MPT) models are applied to groups of homogeneous participants, where all participants within a group are assumed to have identical MPT model parameter values. This assumption is unreasonable when MPT models are used for clinical assessment, and it often may be suspect for applications to ordinary psychological experiments. One method for dealing with parameter variability is to incorporate random effects assumptions into a model. This is achieved by assuming that participants’ parameters are drawn independently from some specified multivariate hyperdistribution. In this paper we explore the assumption that the hyperdistribution consists of independent beta distributions, one for each MPT model parameter. These beta-MPT models are ‘hierarchical models’, and their statistical inference is different from the usual approaches based on data aggregated over participants. The paper provides both classical (frequentist) and hierarchical Bayesian approaches to statistical inference for beta-MPT models. In simple cases the likelihood function can be obtained analytically; however, for more complex cases, Markov Chain Monte Carlo algorithms are constructed to assist both approaches to inference. Examples based on clinical assessment studies are provided to demonstrate the advantages of hierarchical MPT models over aggregate analysis in the presence of individual differences.     

A New Model for Acquiescence at the Interface of Psychometrics and Cognitive Psychology

ABSTRACT

When measuring psychological traits, one has to consider that respondents often show content-unrelated response behavior in answering questionnaires. To disentangle the target trait and two such response styles, extreme responding and midpoint responding, Böckenholt (2012a Böckenholt, U. (2012a). Modeling multiple response processes in judgment and choice. Psychological Methods, 17, 665–678. doi:10.1037/a0028111[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) developed an item response model based on a latent processing tree structure. We propose a theoretically motivated extension of this model to also measure acquiescence, the tendency to agree with both regular and reversed items. Substantively, our approach builds on multinomial processing tree (MPT) models that are used in cognitive psychology to disentangle qualitatively distinct processes. Accordingly, the new model for response styles assumes a mixture distribution of affirmative responses, which are either determined by the underlying target trait or by acquiescence. In order to estimate the model parameters, we rely on Bayesian hierarchical estimation of MPT models. In simulations, we show that the model provides unbiased estimates of response styles and the target trait, and we compare the new model and Böckenholt’s model in a recovery study. An empirical example from personality psychology is used for illustrative purposes.